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In Chapter 13, a symmetrical assembly of 12 hexagonal sticks and dowels was broken into various sub-units with fewer and shorter sticks and dowels. By the same token, the assembly of 30 pentagonal sticks and dowels can be broken into interesting sub-units. One such is shown in Fig. 154 using five identical sticks and five dowels. Each stick has four holes. The assembly has fivefold symmetry. One puzzling version of it uses two elbow pieces.
Fig. 154
Note the interesting genealogy of the above offspring. It represents the conjugation of two distinctly different ideas - the pentagonal geometry of this chapter and the sub-unit scheme of Chapter 13, each with its own separate line of development, surprisingly and fortuitously joining neatly together. This happens all the time in the field of geometrical dissections and is just one more reason why this recreation is so fascinating.
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